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%I #7 Oct 31 2018 05:32:28
%S 71,1187,9500,49355,193179,619132,1710198,4211175,9462805,19735067,
%T 38684438,71962709,128007725,219049200,362365540,581830389,909790395,
%U 1389318475,2076889640,3045529223,4388486135,6223486556,8697626250
%N Number of length 4+4 0..n arrays with no consecutive five elements summing to more than 2*n.
%H R. H. Hardin, <a href="/A241940/b241940.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1391/20160)*n^8 + (197/252)*n^7 + (1819/480)*n^6 + (3719/360)*n^5 + (5593/320)*n^4 + (1369/72)*n^3 + (66343/5040)*n^2 + (2257/420)*n + 1.
%F Conjectures from _Colin Barker_, Oct 31 2018: (Start)
%F G.f.: x*(71 + 548*x + 1373*x^2 + 623*x^3 + 222*x^4 - 83*x^5 + 36*x^6 - 9*x^7 + x^8) / (1 - x)^9.
%F a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.
%F (End)
%e Some solutions for n=4:
%e ..3....0....1....0....1....1....0....0....0....1....0....3....1....0....1....3
%e ..2....1....4....0....0....0....3....2....2....0....0....1....3....2....3....1
%e ..1....3....0....1....0....1....0....0....0....1....4....0....1....2....2....0
%e ..0....1....0....1....4....2....1....0....2....1....0....0....1....2....0....4
%e ..0....1....3....0....1....0....2....0....0....0....0....1....0....1....0....0
%e ..3....0....0....0....1....2....1....1....1....2....2....4....2....0....0....3
%e ..2....1....0....1....1....0....0....4....1....0....2....2....0....0....1....1
%e ..1....4....3....2....0....1....0....3....4....3....3....1....1....3....1....0
%Y Row 4 of A241936.
%K nonn
%O 1,1
%A _R. H. Hardin_, May 02 2014
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